Accuracy Analysis Considering Clearances and Elastic Deformations in Parallel Manipulators

2011 ◽  
Author(s):  
Jokin Aginaga ◽  
Oscar Altuzarra ◽  
Erik Macho ◽  
Jon Olza
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Linear Analysis ◽  
Accuracy Analysis ◽  
Elastic Deformations ◽  
End Effector ◽  
Planar Mechanism ◽  
General Methodology ◽  
Pick And Place ◽  
Mechanical Components

Clearances at joints and deformability of links produce a loss of accuracy when positioning a mechanism. End-effector pose error depends on the mechanism configuration, the applied external wrenches, the nature and magnitude of clearances and the rigidity of the mechanical components. Clearance magnitudes and elastic deformations are much smaller than other dimensions and consequently they are assumed to be infinitesimal, which leads to a linear analysis. Under this assumption, velocity equations can be utilized instead of position ones, and they can be easily expressed by using screw coordinates. A general methodology for analyzing the pose accuracy of a parallel manipulator is presented, making use of the example of a 5R planar mechanism along a pick-and-place trajectory.

Assessing Position Error Due to Clearances and Deformations of Links in Parallel Manipulators

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Jokin Aginaga ◽  
Oscar Altuzarra ◽  
Erik Macho ◽  
Xabier Iriarte
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Position Error ◽  
Elastic Deformations ◽  
End Effector ◽  
Pick And Place ◽  
Smooth Movement ◽  
Mechanical Components

Two of the main sources of position error in parallel manipulators are clearances at joints and elastic deformations of the links. The former are usually necessary in order to produce a smooth movement between the pin and the hub of a joint. The latter are unavoidable and they tend to be greater in manipulators designed for pick-and-place tasks due to the need of light links. It can be stated that the end-effector pose error depends on the mechanism configuration, the applied external wrenches, the nature and magnitude of clearances, and the rigidity of the mechanical components. This paper proposes a procedure to calculate position error in parallel manipulators due to both clearances and elastic deformations. Although the procedure is applicable to any planar or spatial parallel manipulator, a planar 5R mechanism is used as an illustrative example in order to make it easier to understand.

Accuracy Analysis of Parallel Manipulators With Joint Clearance

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Jian Meng ◽  
Dongjun Zhang ◽  
Zexiang Li
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problem ◽  
Parallel Manipulators ◽  
Joint Clearance ◽  
Error Prediction ◽  
Accuracy Analysis ◽  
Analysis Problem ◽  
Convex Optimization Problem ◽  
End Effector ◽  
Position And Orientation

Due to joint clearance, a parallel manipulator’s end-effector exhibits position and orientation (or collectively referred to as pose) errors of various degrees. This paper aims to provide a systematic study of the error analysis problem for a general parallel manipulator influenced by joint clearance. We propose an error prediction model that is applicable to planar or spatial parallel manipulators that are either overconstrained or nonoverconstrained. By formulating the problem as a standard convex optimization problem, the maximal pose error in a prescribed workspace can be efficiently computed. We present several numerical examples to show the applicability and the efficiency of the proposed method.

Kinematics of a Particular 3T1R Parallel Manipulator of Type 2PRPU

2017 ◽  
Author(s):  
Henrique Simas ◽  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
End Effector ◽  
Serial Robots ◽  
Fixed Direction ◽  
Pick And Place ◽  
Displacement Group ◽  
4 Degrees Of Freedom

Schoenflies-motion generators (SMGs) are 4-degrees-of-freedom (dof) manipulators whose end effector can perform translations along three independent directions, and rotations around one fixed direction (Schoenflies motions). Such motions constitute the 4-dimensional (4-D) Schoenflies subgroup of the 6-D displacement group. The most known SMGs are the serial robots named SCARA. Pick-and-place tasks are typical industrial applications that SMGs can accomplish. In the literature, 3T1R parallel manipulators (PMs) have been also proposed as SMGs. Here, a somehow novel 3T1R PM is presented and studied. Its finite and instantaneous kinematics are analyzed in depth, and analytic and geometric tools that are useful for its design are presented. The proposed SMG has a single-loop not-overconstrained architecture with actuators on or near the base and can make the end effector perform a complete rotation.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Analysis and Validation of a Flexible Planar Two Degrees-of-Freedom Parallel Manipulator With Structural Passive Compliance

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Genliang Chen ◽  
Zhuang Zhang ◽  
Lingyu Kong ◽  
Hao Wang
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Interaction Force ◽  
Flexible Manipulator ◽  
End Effector ◽  
Flexible Links ◽  
Wide Range ◽  
Pick And Place ◽  
Passive Compliance ◽  
Large Deflection Problem

Abstract Passive compliance plays an important role in robot pick-and-place manipulation where large interaction force will be produced in response to small misalignments. In this paper, the authors report on compliance analysis and validation of a novel planar pick-and-place parallel manipulator consisting of a flexible limb. In the proposed manipulator, a planar flexible parallelogram linkage, which is coupled with a rigid one, is introduced to connect the moving and the base platforms. Since the flexible parallelogram linkage is capable of producing large deformation in both the horizontal and the vertical directions, the end effector of the manipulator can generate wide-range motions because of the flexible links. An efficient approach to the large deflection problem of flexible links is used to precisely predict the kinetostatics of the manipulator. Then, a compensation algorithm to the structural deflection of the links can be developed to actively control the position of the parallel manipulator’s end effector. The merit of the proposed flexible manipulator is its intrinsic passive compliance while performing pick-and-place tasks. A prototype is fabricated to conduct experiments for the validation of the proposed idea. The results show that the prototype has acceptable positioning accuracy, even when a large external load is exerted on its end effector. The compliance properties of the proposed flexible manipulator have also been verified in both the horizontal and the vertical directions.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

Enlarging operational workspaces in parallel manipulators by connecting working modes. Application to the 3RSS robot

Robotica ◽  
2012 ◽  
Vol 31 (4) ◽  
pp. 539-548 ◽  
Author(s):  
E. Macho ◽  
O. Altuzarra ◽  
C. Pinto ◽  
A. Hernández
Keyword(s):  
Path Planning ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Loss Of Control ◽  
General Methodology

SUMMARYThe aim of this paper is to describe a general methodology for enlarging the workspace within which a parallel manipulator can move in a controllable way. The basis for obtaining this consists in superimposing all the singularity-free regions associated with the various different robot working modes. These can be connected because such transitions do not imply a loss of control of the manipulator. This enlarged operational workspace is associated with a certain assembly mode. In addition, the strategy to be used for path planning in this kind of workspace is presented.

A new family of spherical parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
New Family ◽  
Geometric Conditions ◽  
Singularity Locus ◽  
The Given ◽  
Spherical Parallel Manipulator ◽  
Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

An optimal singularity-free motion planning method for a 6-DOF parallel manipulator

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shiqi Li ◽  
Dong Chen ◽  
Junfeng Wang
Keyword(s):  
Particle Swarm Optimization ◽  
Motion Planning ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Free Motion ◽  
Motion Path ◽  
Swarm Optimization ◽  
End Effector ◽  
Content Type ◽  
Multi Objective

Purpose This paper aims to present a method of optimal singularity-free motion planning under multiple objectives and multiple constrains for the 6-DOF parallel manipulator, which is used as an execution mechanism for the automated docking of components. Design/methodology/approach First, the distribution characteristics of the Jacobian matrix determinant in local workspace are studied based on the kinematics and a sufficient and necessary condition of singularity-free path planning in local workspace is proposed. Then, a singularity-free motion path of the end-effector is generated by a fifth-order B-spline curve and the corresponding trajectories of each actuator are obtained via the inverse kinematics. Finally, several objective functions are defined to evaluate the motion path and an improved multi-objective particle swarm optimization algorithm-based on the Pareto archive evolution is developed to obtain the optimal singularity-free motion trajectories. Findings If the initial pose and the target pose of the end-effector are both singularity-free, a singularity-free motion path can be planned in the local workspace as long as all the values of each pose elements in their own directions are monotonous. The improved multi-objective particle swarm optimization (IMPSO) algorithm is effective and efficient in the optimization of multi-objective motion planning model. The optimal singularity-free motion path of the end-effector is verified in the component docking test. The docking result is that the movable component is in alignment with the fixed one, which proves the feasibility and practicability of the proposed motion path method to some extent. Originality/value The proposed method has a certain novelty value in kinematic multi-objective motion planning of parallel manipulators; it also increases the application prospect of parallel manipulators and provides attractive solutions to component assembly for those organizations with limited cost and that want to find an option that is effective to be implemented.

scholarly journals Simulation and Optimisation of a Two Degree of Freedom, Planar, Parallel Manipulator

2021 ◽  
Author(s):  
◽  
Ben Haughey
Keyword(s):  
Genetic Algorithm ◽  
Simulation Model ◽  
Cycle Time ◽  
Parallel Manipulator ◽  
Robotic Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Planar Parallel Manipulator ◽  
Pick And Place ◽  
Two Degree Of Freedom

<p>Development in pick-and-place robotic manipulators continues to grow as factory processes are streamlined. One configuration of these manipulators is the two degree of freedom, planar, parallel manipulator (2DOFPPM). A machine building company, RML Engineering Ltd., wishes to develop custom robotic manipulators that are optimised for individual pick-and-place applications. This thesis develops several tools to assist in the design process. The 2DOFPPM’s structure lends itself to fast and accurate translations in a single plane. However, the performance of the 2DOFPPM is highly dependent on its dimensions. The kinematics of the 2DOFPPM are explored and used to examine the reachable workspace of the manipulator. This method of analysis also gives insight into the relative speed and accuracy of the manipulator’s end-effector in the workspace. A simulation model of the 2DOFPPM has been developed in Matlab’s® SimMechanics®. This allows the detailed analysis of the manipulator’s dynamics. In order to provide meaningful input into the simulation model, a cubic spline trajectory planner is created. The algorithm uses an iterative approach of minimising the time between knots along the path, while ensuring the kinematic and dynamic limits of the motors and end-effector are abided by. The resulting trajectory can be considered near-minimum in terms of its cycle-time. The dimensions of the 2DOFPPM have a large effect on the performance of the manipulator. Four major dimensions are analysed to see the effect each has on the cycle-time over a standardised path. The dimensions are the proximal and distal arms, spacing of the motors and the height of the manipulator above the workspace. The solution space of all feasible combinations of these dimensions is produced revealing cycle-times with a large degree of variation over the same path. Several optimisation algorithms are applied to finding the manipulator configuration with the fastest cycle-time. A random restart hill-climber, stochastic hill-climber, simulated annealing and a genetic algorithm are developed. After each algorithm’s parameters are tuned, the genetic algorithm is shown to outperform the other techniques.</p>

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